Strong Euler Wellcomposedness

Authors

Nicolas Boutry, Rocio Gonzalez-Diaz, Maria-Jose Jimenez, Eduardo Paluzo-Hildago

Journal

Journal of Combinatorial Optimization

Type

article

Publisher

Springer

Projects

Olena

Keywords

Image

Date

2021-11-23

Abstract

In this paper, we define a new flavour of well-composedness, called strong Euler well-composedness. In the general setting of regular cell complexes, a regular cell complex of dimension $n$ is strongly Euler well-composed if the Euler characteristic of the link of each boundary cell is $1$, which is the Euler characteristic of an $(n-1)$-dimensional ball. Working in the particular setting of cubical complexes canonically associated with $n$-D pictures, we formally prove in this paper that strong Euler well-composedness implies digital well-composedness in any dimension $n\geq 2$ and that the converse is not true when $n\geq 4$.

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Bibtex (lrde.bib)

@Article{	  boutry.21.joco,
  author	= {Nicolas Boutry and Rocio Gonzalez-Diaz and Maria-Jose
		  Jimenez and Eduardo Paluzo-Hildago},
  title		= {Strong {E}uler Wellcomposedness},
  journal	= {Journal of Combinatorial Optimization},
  month		= nov,
  year		= {2021},
  abstract	= {In this paper, we define a new flavour of
		  well-composedness, called strong Euler well-composedness.
		  In the general setting of regular cell complexes, a regular
		  cell complex of dimension $n$ is strongly Euler
		  well-composed if the Euler characteristic of the link of
		  each boundary cell is $1$, which is the Euler
		  characteristic of an $(n-1)$-dimensional ball. Working in
		  the particular setting of cubical complexes canonically
		  associated with $n$-D pictures, we formally prove in this
		  paper that strong Euler well-composedness implies digital
		  well-composedness in any dimension $n\geq 2$ and that the
		  converse is not true when $n\geq 4$.},
  publisher	= {Springer},
  pages		= {3038--3055},
  volume	= {12148},
  issue		= {44},
  doi		= {10.1007/s10878-021-00837-8}
}